The MID property for a second-order neutral time-delay differential equation

This paper considers the Multiplicity-Induced-Dominancy (MID) property for second order neutral time-delay differential equations. Necessary and sufficient conditions for the existence of a root of maximal multiplicity are given in terms of this root and the parameters (including the delay) of the given equation. Links with dominancy of this root and with the exponential stability property of the solution of the considered equations are given. Finally, we illustrate the obtained results on the classical oscillator control problem.